No calculus knowledge a crazy state of affairs

 In AMSI in the news, News

Article by Tim Dodd, Australian Financial Review, 10 August 2015

Bruce Henry, the head of UNSW Australia’s School of Mathematics and Statistics laments that 70 per cent of students now finish high school without any knowledge of calculus.

Is this a problem? Definitely.

We hear enough about how appalling it is that students in schools and universities have a lack of grounding in our political, social and legal heritage; that they lack the historical context to understand why we are where we are today.

That’s exactly why calculus should also be part of a basic, broad education. Calculus was a signal advance in maths, invented separately by Isaac Newton and Gottfried Leibniz in the 17th century. For the first time people could write mathematical equations that were able to relate not just quantities to each other, but rates of changes of quantities.

It enabled Newton to calculate the orbits of the planets using his theory of gravity and it opened up a rich field of applications for mathematics. Understanding electricity and magnetism would be impossible without calculus. In fact, most of modern technology wouldn’t exist without it.

That’s why giving high school students an understanding of calculus is important. Surely more than 30 per cent of students are capable of studying it. And, for the others, it’s at least important to understand what it is.

Henry points to another reason why calculus is important to study today. Calculus is not only key to understanding our current technology, but to developing future technology. At the moment huge strides are being made in statistics, a field with the generic name of “big data”.

STATISTICS UNDERPINNED BY CALCULUS

“But really, modern statistics – which is where the future is going increasingly – is underpinned by calculus. It’s increasingly important that students are taught calculus,” Henry says.

In fact, statistics is another area in which mathematics teaching has badly let down school students. All of us are bombarded daily by statistical claims, many of them spurious or misleading, and too few of us are sufficiently knowledgeable to separate the truth from the fiction.

The fact that “97 per cent fat-free” is an effective, emotionally appealing slogan for food manufacturers speaks of the lack of critical thinking about statistics. Are we happy if our food contains 3 per cent pure fat?

Fortunately, in the changes to the national school curriculum being developed, statistics is being given more focus.

But this brings us back to the question. Should maths be a compulsory subject in year 12? Not everyone can do maths well. But shouldn’t maths at least be taught as a life skill and as an important foundation subject at that level?

Henry thinks so. “English is compulsory, and shouldn’t mathematics be compulsory as a companion instrument to understand the world,” he asks rhetorically.

Interestingly federal Education Minister Christopher Pyne, long an advocate of giving school students more foundational understanding of history and other humanities subjects, now appears to see the need for it in maths and science.

Earlier this year he put to state governments – which actually run public schools – a plan to make maths and science compulsory to year 12. The states, unfortunately, knocked him back.

SCHOOLS LAPSE AS UNI REQUIREMENTS REDUCE

But maths in schools needs to be bolstered at more than just the foundational level. Worryingly, year 12 students have been making a long-term shift away from intermediate and advanced maths – the very subjects that teach calculus.

In the past 20 years the proportions studying intermediate maths in year 12 has fallen from about 27 per cent to 19 per cent, and the number studying advanced maths (which builds on intermediate) has fallen from about 14 per cent to 10 per cent.

One reason that year 12 students see no need to do intermediate or advanced maths is that an increasing number of universities no longer require it to enter degrees such as science, engineering and commerce, for which mathematical knowledge is necessary.

In NSW no universities require maths to enter any of these degrees, even engineering. So if universities are not insisting that students study calculus in year 12, even to enter courses in which calculus features heavily, why should they do it?

It’s a crazy state of affairs, in which universities – the institutions we rely on to develop and preserve high level knowledge – happily sabotage their own standards in pursuit of student numbers.

Those universities that have dropped maths prerequisites argue they are offering an avenue for bright students who may have attended a poor school at which maths was taught badly.

Second chances are to be encouraged, but they should be the exception rather than the rule. Universities need to bring back maths as a prerequisite for degrees that need it.

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